Kurz: Hybridní systémy - B231

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Vybrat sekci General information about the course

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General information about the course

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Vybrat sekci Discrete-event systems: (finite) state automata as a model of discrete-event systems

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Discrete-event systems: (finite) state automata as a model of discrete-event systems
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Vybrat sekci Petri nets and their use for modelling, analysis and control of discrete-event systems

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Petri nets and their use for modelling, analysis and control of discrete-event systems
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Vybrat sekci (max,+) algebra and its use for modelling, analysis and control of (some) discrete-event systems

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(max,+) algebra and its use for modelling, analysis and control of (some) discrete-event systems
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Vybrat sekci Hybrid automata as the key modeling framework for hybrid systems

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Hybrid automata as the key modeling framework for hybrid systems
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Vybrat sekci Hybrid equations as an alternative modeling framework for hybrid systems

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Hybrid equations as an alternative modeling framework for hybrid systems
Also known as flow-jump equations or flow-event equations.
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Vybrat sekci Subclasses of hybrid systems: Reset (control) systems, Switched/switching dynamical systems, Piecewise Affine (PWA) Systems. Definitions and conditions of existence and uniqueness of a solution

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Subclasses of hybrid systems: Reset (control) systems, Switched/switching dynamical systems, Piecewise Affine (PWA) Systems. Definitions and conditions of existence and uniqueness of a solution
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Vybrat sekci Concept(s) of a solution of a hybrid system, conditions of existence

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Concept(s) of a solution of a hybrid system, conditions of existence
Hybrid executions.
Existence and uniqueness of solution of discontinuous differential equations.
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Vybrat sekci Analysis of stability of hybrid systems I.: common Lyapunov function (CLF)

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Analysis of stability of hybrid systems I.: common Lyapunov function (CLF)
Common quadratic Lyapunov function (CQLF) using linear matrix inequalities (LMI) and semidefinite programming (SDP),
Common higher-degree polynomial Lyapunov function using positive polynomial optimization via sum-of-squares (SOS) programming.
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- Vybrat aktivitu Literature for LMI, SDP and SOS programming
  
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Vybrat sekci Analysis of stability of hybrid systems II.: multiple Lyapunov function (MLF)

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Analysis of stability of hybrid systems II.: multiple Lyapunov function (MLF)
Piecewise quadratic/polynomial Lyapunov function via S-procedure.
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Vybrat sekci Complementarity dynamical systems

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Complementarity dynamical systems
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Vybrat sekci Mixed logical dynamical (MLD) description of discrete-time dynamical systems

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Mixed logical dynamical (MLD) description of discrete-time dynamical systems
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Vybrat sekci MPC for hybrid dynamical systems

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MPC for hybrid dynamical systems
Within the MLD framework
online MPC for MLD
explicit (offline) MPC for MLD via multiparametric programming
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Vybrat sekci Formal verification of hybrid systems

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Formal verification of hybrid systems
Safety requirements (invariance)
Verification via reachability analysis
by checking feasibility of optimal control for MLD
by set propagation techniques
Verification via barrier certificates
Liveness (progress) requirements
General specifications through temporal logics: LTL, CTL, ...
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Vybrat sekci Variable structure systems and Sliding mode control

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Variable structure systems and Sliding mode control

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